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"Epicycles" are the fiction dreamed up by pre-Copernican
astronomers to permit them to discount the evidence of their own eyes - the
observed motion of the nearby planets is clearly at odds with anything other
than a heliocentric view of the universe, but until the 17th century these
complex, almost coiled orbits were the only thing that could keep the
earth in its rightful place at the centre of the solar system.

For more information, try these
two
pages, part of the University of Tennessee's online syllabus for their Astronomy
161 course, or this wonderful little
Java
applet at The University of Syracuse Department of Physics.